Complete The Square Without Fractions

TL;DR

This video introduces a new method for completing the square, found in an 1800s math book, to avoid fractions and simplify equations.

Transcript

in this video i'm going to show you a new way of completing the square so this is not something that i created this is something i found in a book from the 1800s and we'll talk a little bit about the book later in this video but for now let's just jump into the process and let me explain the math behind this method and we'll do a couple examples an... Read More

Key Insights

• ✋ The new method for completing the square involves multiplying the equation by four times the coefficient of the highest power of the unknown quantity.
• 😒 This method can simplify equations and avoid the use of fractions.
• ❎ The process includes squaring the coefficient of the unknown quantity and adding it to both sides, resulting in a perfect square trinomial.

Questions & Answers

Q: What is the first step in completing the square using this new method?

The first step is to multiply the equation by four times the coefficient of the highest power of the unknown quantity.

Q: How is the equation transformed into a perfect square trinomial?

After multiplying the equation, the coefficient of the unknown quantity is squared and added to both sides, resulting in a perfect square trinomial.

Q: What is the significance of using this method over the traditional method for completing the square?

This method can avoid fractions and provide a simpler solution to the equation.

Q: Where can the 1800s math book, which introduces this method, be found?

The book, titled "Elements of Algebra" by Milne, is available for free online and contains answers to all the problems.

Summary & Key Takeaways

• The video demonstrates a new method for completing the square, involving multiplying the equation by four times the coefficient of the highest power of the unknown quantity and adding the square of the coefficient of the first power.

• The method is applied to examples, showing how the equation can be simplified into a perfect square trinomial.

• The video highlights the benefits of this method, including avoiding fractions and providing a straightforward solution to the equation.